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Hi, I'm using the following definition for the Fourier transform.

[tex]

F\left( q \right) = \int\limits_{ - \infty }^\infty {e^{iqx} f\left( x \right)dx}

[/tex]

(I used a capital F instead of f with a squiggle on top because the tex code doesn't seem to be working the way I intended it to.)

I have the function

[tex]

f\left( x \right) = \left\{ {\begin{array}{*{20}c}

{1,a < x < b} \\

{0,otherwise} \\

\end{array}} \right.

[/tex]

So [tex]F\left( q \right) = \int\limits_{ - \infty }^\infty {e^{iqx} f\left( x \right)dx} [/tex]

[tex] = \int\limits_a^b {e^{iqx} dx} [/tex]

[tex]

= \frac{i}{q}\left( {e^{iqa} - e^{iqb} } \right)

[/tex]

According to the definition I'm using, is this the correct answer? I ask this because I'm not given an answer and I need to verify my answer by using the inverse Fourier transform. I haven't done complex analysis so integrals of ratios of exponentials and polynomials aren't things I can deal with right now. Which is why I'd like to know if I've taken the correct approach so that I can at least get through some questions.

Any help would be good thanks.

[tex]

F\left( q \right) = \int\limits_{ - \infty }^\infty {e^{iqx} f\left( x \right)dx}

[/tex]

(I used a capital F instead of f with a squiggle on top because the tex code doesn't seem to be working the way I intended it to.)

I have the function

[tex]

f\left( x \right) = \left\{ {\begin{array}{*{20}c}

{1,a < x < b} \\

{0,otherwise} \\

\end{array}} \right.

[/tex]

So [tex]F\left( q \right) = \int\limits_{ - \infty }^\infty {e^{iqx} f\left( x \right)dx} [/tex]

[tex] = \int\limits_a^b {e^{iqx} dx} [/tex]

[tex]

= \frac{i}{q}\left( {e^{iqa} - e^{iqb} } \right)

[/tex]

According to the definition I'm using, is this the correct answer? I ask this because I'm not given an answer and I need to verify my answer by using the inverse Fourier transform. I haven't done complex analysis so integrals of ratios of exponentials and polynomials aren't things I can deal with right now. Which is why I'd like to know if I've taken the correct approach so that I can at least get through some questions.

Any help would be good thanks.

Last edited: